President Obama is still reaping the dividends from this month’s fight with the House GOP on extending the payroll tax.

Obama’s approval ratings are higher than his disapproval ratings for the first time since July, according to the latest Gallup Poll. About 47% of Americans approve of the way he is doing his job, while 45% disapprove of his performance. The three-day tracking poll was conducted Dec. 21-23.

The polling was finalized on Dec. 23 as House Republicans agreed — after initially resisting — to a two-month payroll tax patch that will extend 2011 rates for 160 millions for the first two months of the new year. House Republicans faced stinging criticism from Obama and Democrats after rank-and-file Republicans initially blocked the short-term bipartisan deal hammered out in the Senate.

The last time that Obama’s approval rating was higher than his disapproval rating was during the July 7-9 tracking period.

This magic line for an incumbent president is not precise, but can be considered to be at about the 48% mark, according to Gallup.